THE ANALYTICITY DOMAIN OF SPECTRAL DENSITY OF THE ELECTROMAGNETIC FIELD IN A VERTICALLY INHOMOGENEOUS CONDUCTIVE MEDIUM

The electromagnetic field in electrical exploration problems is often represented as integrals with a fast-oscillating nucleus. When calculating these integrals on a computer, it is necessary to deform the contour of integration into the plane of the complex variable. The article studies the allowable deformation region of the integration contour in the case of a non-uniform medium, in which strong and weak solutions of electromagnetic field are analytical. The source of the field is a vertical dipole. A similar problem was solved for a horizontally layered medium with a harmonious electrical or magnetic dipole as a source.

An approximate solution of the one class third order onlinear differential equation in the analyticity domain

В работе рассмотрен класс нелинейных дифференциальных уравнений третьего порядка с полиномиальной правой частью шестой степени. Доказана теорема существования и единственности решения в области аналитичности. Построено аналитическое приближенное решение. Предложен вариант оптимизации априорных оценок с помощью апостериорных. Проведен численный эксперимент. There is a class of third-order nonlinear differential equations with polynomial right part of the sixth degree considered in the paper. The existence and uniqueness theorem of a solution in the domain of analyticity is proved by authors. There is an analytical approximate solution which was constructed by V. Orlov and R. Razakova. A variant of optimization of a priori estimates using posterior ones is proposed by authors. A numerical experiment is carried out too.